What is integral from b to a of f(x) ?

The answer to integral from b to a of f(x) is (f(a^2-b^2))/2

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integral from b to a of f(x)

\int_{b}^{a} f (x) d x

\frac{f ( a ^{2} - b ^{2} )}{2}

Solution steps

\int_{b}^{a} f x d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= f \cdot \int_{b}^{a} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{b}^{a}

= f [\frac{x ^{2}}{2}]_{b}^{a}

Compute the boundaries:

\frac{a ^{2}}{2} - \frac{b ^{2}}{2}

= f (\frac{a ^{2}}{2} - \frac{b ^{2}}{2})

Simplify

= \frac{f ( a ^{2} - b ^{2} )}{2}

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What is integral from b to a of f(x) ?
The answer to integral from b to a of f(x) is (f(a^2-b^2))/2